Lupaş blending functions with shifted knots and q -Bézier curves

[摘要] In this paper, we introduce blending functions of Lupaş q-Bernstein operators with shifted knots for constructing q-Bézier curves and surfaces. We study the nature of degree elevation and degree reduction for Lupaş q-Bézier Bernstein functions with shifted knots for $t \in [\frac{a}{[\mu ]_{q}+b} , \frac{[\mu ]_{q}+a}{[\mu ]_{q}+b} ]$ . For the parameters $a=b=0$ , we get Lupaş q-Bézier curves defined on $[0,1]$ . We show that Lupaş q-Bernstein functions with shifted knots are tangent to fore-and-aft of its polygon at end points. We present a de Casteljau algorithm to compute Bernstein Bézier curves and surfaces with shifted knots. The new curves have some properties similar to q-Bézier curves. Similarly, we discuss the properties of the tensor product for Lupaş q-Bézier surfaces with shifted knots over the rectangular domain.

[学科分类] 电力

[关键词] q -integers;Degree elevation;De Casteljau-type algorithm;Lupaş q -Bernstein operators with shifted knots;Bézier curve;Tensor product;Shape preserving